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Maximal and variational principles in vector spaces. (English) Zbl 1337.49008

Daras, Nicholas J. (ed.) et al., Computation, cryptography, and network security. Cham: Springer (ISBN 978-3-319-18274-2/hbk; 978-3-319-18275-9/ebook). 525-575 (2015).
Summary: In Section 1, a separable type extension of Ekeland’s variational principle from 1974 is given in the realm of ordered convergence spaces. The connections with a related statement of Khanh from 1989 are then discussed. In Section 2, the Brezis-Browder ordering principle from 1976 is used to establish a lot of maximality results in triangular structures due to Pasicki (from 2011). Finally, in Section 3, some technical aspects of the variational principle due to Bao and Mordukhovich (from 2007) are being analyzed. Further, an extension of this result is proposed, by means of a pseudometric maximal principle of the author from 2008.
For the entire collection see [Zbl 1329.94003].

MSC:

49J27 Existence theories for problems in abstract spaces
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
46A40 Ordered topological linear spaces, vector lattices
54E35 Metric spaces, metrizability
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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